complex internal vertices
BoolTool add-on

I'm not sure on what you mean by saying polyverts, but I'm am assuming that is something similar to parenting+vertex duplication...



So starting from a similar situation, after make the duplicate real, we have a plenty of different objects.

Download and install the BoolTool add-on that will allow us to merge all the objects with boolean operation.

Select all the objects, make the base mesh the active object (the biggest one: it's important that this object has at least a piece of volume in common with every sphere object) and choose from BoolTool tool tab the Direct Union tool.



It will take a while (depending on the number of spheres,their resolution and your hardware...for me about 15 minutes), but the result is quite good, clean and, above all, watertight.



Below a view of the insight. Notice how there is only a shell. The internal faces do not exist anymore.